Compound

What Is Compound?

Compound, to savers and investors, means the ability of a sum of money to grow exponentially over time by the repeated addition of earnings to the principal invested. Each round of earnings adds to the principal that yields the next round of earnings. In savings accounts, this is called compound interest.

By contrast, simple interest does not reflect compounding. The interest is paid on the original balance only, not the original balance plus its previous earnings.

Key Takeaways

  • Compounding is the repeated addition of interest payments to the principal invested over a period of time.
  • The principal grows exponentially as each new payment of interest is added to it.
  • The higher the number of compounding periods, the greater the amount of compound interest will be.
  • Financial experts advise individuals to start saving early as the benefits of time with compounding greatly increases returns.
  • Simple interest is paid only on the original amount invested, growing more slowly over time.
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Understanding Compound Interest

Understanding Compound

Suppose you invest $10,000 into company XYZ. In the first year, the shares rose 20%. Your investment is now worth $12,000. Based on its good performance, you hold onto the stock. In Year 2, the shares appreciate another 20%. Your $12,000 investment has now grown to $14,400.

Rather than your shares appreciating an additional $2,000 (20%) as they did in the first year, they appreciate an additional $400, because the $2,000 you gained in the first year grew by 20% as well.

If you extrapolate the process out, the numbers start to get very big as your previous earnings start to provide further returns. In fact, $10,000 invested at 20% annually for 25 years would grow to nearly $1,000,000, and that's without adding any money to the original amount invested.

The power of compounding was called the eighth wonder of the world by Albert Einstein, or so the story goes. He also is said to have declared: "He who understands it, earns it. He who doesn't, pays it."

How to Calculate Compound Interest

The formula for calculating compound interest is as follows:

Compound Interest = Total amount of Principal and Interest in future (or Future Value) less Principal amount at present (or Present Value)
= [P (1 + i)n] – P
= P [(1 + i)n – 1]
Where P = Principal, i = nominal annual interest rate in percentage terms, and n = number of compounding periods.

Don't forget to adjust the "i" and "n" if the number of compounding periods is more than once a year.

Example of Compound Interest

Take a three-year loan of $10,000 at an interest rate of 5% that compounds annually. What would be the amount of interest? In this case, it would be as follows:

$10,000 [(1 + 0.05)3] – 1 = $10,000 [1.157625 – 1] = $1,576.25

When calculating compound interest, the number of compounding periods makes a significant difference. The higher the number of compounding periods, the greater the amount of compound interest will be.

If the number of compounding periods is more than once a year, "i" and "n" must be adjusted accordingly. The "i" must be divided by the number of compounding periods per year, and "n" is the number of compounding periods per year times the loan or deposit’s maturity period in years.

Investor.gov, a website operated by the U.S. Securities and Exchange Commission, offers a free online compound interest calculator. The calculator allows the input of monthly deposits made to the principal, which is helpful for regular savers.

Compound Interest vs. Simple Interest

Simple interest only takes into account the principal balance of a loan or deposit, whereas compound interest takes into account the principal balance and the interest that has accumulated over a specific period of time.

For example, if an individual borrows $15,000 over a four-year period with an annual interest rate of 5%, the simple interest would only be calculated on the $15,000, as opposed to compound interest, which would be $15,750 (15,000 x .05) after the first year, and $16,537.5 (15,450 x .05) after the second year, and $17,364.4 (16,537.5 x .05) after the third year.

As an individual borrowing money, it is better to have your loan as a simple interest loan. As an individual looking to save, it is better if your investments are compounding.

With simple interest, the total amount of interest would be 15,000 x .05 x 3 =$2,250, and the total amount owed would be $15,000 + $2,250 = $17,250; $114 less than if the loan was based on compound interest.

What Is the Compound Annual Growth Rate?

The compound annual growth rate is a representational growth rate that is the rate of return that is needed for an investment to grow from its beginning balance to its ending balance. It shows the rate that an investment would have grown if the rate of return was the same for every year and if profits were reinvested at the end of every year. It is used as a comparison tool between possible investments as it smooths results.

What Is Discrete Compounding?

Discrete compounding is when interest is calculated and added to the principal amount at set intervals. Common intervals that interest is compounded are weekly, monthly, or yearly. Discrete compounding is contrasted to continuous compounding where interest is compounded continuously—at shorter intervals than discrete compounding.

What Is Continuous Compound Interest?

Continuous compound interest is when interest is calculated and added to the principal amount continuously. It is the most extreme form of compounding as it is done in very short intervals, as opposed to the more common intervals of a week, month, or year. It seeks to compound interest over an infinite number of periods. This is primarily a theoretical concept rather than one of actual practicality.

Do Banks Use Simple Interest or Compound Interest?

Banks can use both compound interest and simple interest, depending on the regulations and type of product. Simple interest is calculated on only the principal amount of the loan whereas compound interest is calculated on both the principal and the interest. To borrow money, it is better to have simple interest loans. To save, it is better to have compound interest investments.

What Is Compound in Crypto?

Compound in crypto relates to a protocol that deals with the borrowing and lending of crypto. It is a decentralized, blockchain-based protocol that facilitates crypto borrowing and lending.

The Bottom Line

Compounding is the ability of money to grow exponentially due to the repeated addition of earnings to the initial investment over time. One round of earnings is added to the overall amount which allows for a larger amount to be invested, generating even more earnings, which are then also invested back into the grown sum, with the process continuously occurring over time, allowing for savings to grow. This is the reason experts advise people to invest as early as they can.

Article Sources

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  1. Goodreads. "Albert Einstein Quotes." Accessed Dec. 10, 2021.

  2. Cryptopedia. "What Is Compound in 5 Minutes." Accessed Dec. 10, 2021.

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